Wait I just now thought of this as it don't explain why her eye is swollen but it sounds like she cou,d have wry neck or something since u say she is holding her head to one side funny I am not sure how to cure it if u want to give it a try and see if it helps her any
It could also be a sinus infection, an eye swollen on the affected side wouldn't surprise me.
I think the other condition is MG....
Sinus infection can create balance problems and cause them to shake their heads trying to relieve the pressure.